A comparison of higher-order generalized eigensystem techniques and Tikhonov regularization for the inverse problem of electrocardiography

In a recent series of papers we proposed a new class of methods, the genera lized eigensystem (GES) methods, for solving the inverse problem of electro cardiography. In this paper, we compare zero, first, and second order regul arized GES methods to zero, first, and second order Tikhonov methods. Both optimal results and results from parameter estimation techniques are compar ed in terms of relative error and accuracy of epicardial potential maps. Re sults from higher order regularization depend heavily on the exact form of the regularization operator, and operators generated by finite element tech niques give the most accurate and consistent results. In the optimal parame ter case, the GES techniques produce smaller average relative errors than t he Tikhonov techniques. However, as the regularization order increases, the difference in average relative errors between the two techniques becomes l ess pronounced. We introduce the minimum distance to the origin (MDO) techn ique to choose the number of expansion modes for the GES techniques. This p roduces average relative errors similar to those obtained using the composi te residual and smoothing operator (CRESO) with Tikhonov regularization. Se cond order regularization gives the smallest average relative errors but ov er-smoothes important epicardial features. In general, GES with MDO resolve s the epicardial features better than Tikhonov with CRESO for the data set studied.